4
Fracture of a Laminated Composite
The fracture mechanisms of UD plies vary strongly depending on the nature of the fiber, matrix, interfaces, stress state and fiber ratio. In this chapter, we will limit ourselves to describing the primary modes of fracture observed on a laminated composite formed of UD plies of resistant and brittle fibers such as glass, carbon or Kevlar and an organic resin that is more ductile than the fiber.
4.1. Fracture of a UD ply
The fracture of a UD ply reveals a fracture scenario that a combination of elementary fractures, namely fiber fracture, matrix cracking and matrix/fiber debonding. These scenarios will be detailed mainly for plane stress.
4.1.1. Longitudinal tension
On this type of UD composite, where the matrix is generally more ductile than the fiber, fracture from longitudinal tension is governed by the fiber fracture. Indeed, the longitudinal strain experienced by the fiber and the matrix being the same, and the strain limit of the fiber being generally lower than the resin, the fiber will break first.
Nonetheless, the fiber being quite brittle, there is a high dispersion of the tensile strength and it will begin to break in a scattered pattern within the test-piece during the second part of the loading, with an increase in the number of broken fibers at the end of the test.
Figure 4.1. Longitudinal tension and schematic curves of stress / strain in the fiber and resin of a composite. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
Figure 4.2. Fracture of a composite with a high a) and low b) interface resistance. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
Once an isolated fiber has broken, this fracture will either cause a transverse crack of the matrix (in the case of a brittle matrix) and high interface resistance (Figure 4.2(a)) which will diffuse stress concentration onto the neighboring fibers, or a fracture of the interface in the case of low interface resistance or of high fiber tensile strength (Figure 4.2(b)). The types of materials currently in use in the aeronautical field present relatively low interface resistance which therefore fracture in this way (Figure 4.2(b)). This also means that the fracture of an isolated fiber is not a problem, as the load is passed on to neighboring fibers (as long as they are not fractured). These local fractures will then multiply and eventually coalesce leading to a catastrophic failure of the UD composite.
Figure 4.3. Micrograph of a fracture facies after longitudinal tensile test [PET 05]
In order to perform these tests, we take care to place tabs on the ends of the tensile test specimen in order to avoid stress concentration in the clamps and ensure that the fracture takes place at the center of the sample.
Figure 4.4. Tensile test specimen, with tabs and strain gauges, of a quasi-UD composite [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
We obtain the stress from the force sensor of the tensile machine and the strain from the strain gauges placed in the central part of the specimen. In the following figure, we observe the difference in behavior between the fiber direction, noted 0°, and the transversal direction, noted 90°.
Figure 4.5. Tensile test at 0° and 90° of a quasi-UD composite [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
4.1.2. Longitudinal compression
During a longitudinal compression test, the fracture is associated with the phenomenon of micro-buckling or kink bands. During the test, we observe buckling of the fibers. This buckling is then stabilized thanks to the presence of the resin (which is loaded in shear). Once the resin reaches its shear stress limit, it will break and cause shear bands or kink bands (Figure 4.6).
In order to perform these tests, we use specimens with specific geometries (with a short useful length in order to avoid premature fracture from buckling) (Figure 4.7). Furthermore, in order to verify that the real stress state of the specimen is compression, we generally use two gauges on both the faces of the specimen in order to isolate the compressive stress by calculating their half-sum, and the bending component by calculating their half-difference. The heavy increase in this bending strain at the end of the test is a result of damage caused to the specimen which causes it to open (Figure 4.8).
Figure 4.6. Longitudinal compression fracture: diagram a) and micrographic cut b) [PIN 06] of a kink band. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
Figure 4.7. Longitudinal compression a) and geometry of the specimen b) [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
Figure 4.8. Longitudinal compression test of a UD composite [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
The compression test is one of the more delicate tests to perform, and we observe a high scattering in the results depending on the geometry of the sample used. The problem arises from the fact that to have an even compression stress state within the specimen, we would need to be able to increase its length (to avoid the boundary effect due to the clamps on the machine); however, that is impossible as we want to avoid the overall buckling of the specimen!
4.1.3. Transverse tension
During the tensile test along the transversal direction of a UD composite, a high stress concentration coefficient within the fiber/matrix interface in the loading direction will lead to the debonding of these interfaces at multiple points of the specimen and, eventually, the coalescence of these cracks will lead to the fracture of the specimen. This type of fracture is probably the most critical fracture mode for a UD, along with shearing. Keep in mind though that UD is designed to work along the fiber direction and that the very design of the structure should avoid this type of loading. In practice, other plies of the laminate should withstand this load. In fact, it’s to avoid this type of fracture that there are at least 10% of fibers in every direction (0°, 45°, −45° and 90°), even non-stressed ones. Furthermore, a moderate fracture is generally non-critical for the structure and can often be tolerated. Obviously, the limit strength in transverse tension is lower to that in longitudinal tension (
Figure 4.8).Figure 4.9. Transverse tension a) and associated damage scenario b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
4.1.4. Transverse compression
During compression in the transversal direction of the UD, a high stress concentration coefficient within the fiber/matrix interface will lead to the debonding of these interfaces at multiple spots within the test specimen and the coalescence of these cracks will lead to the fracture of the specimen. This fracture scenario resembles, upon first glance, that of transverse tension. However, upon closer inspection compression is slightly more complex. We observe a crack at angles between approximately 45° and 60° compared to the load direction.
Figure 4.10. Transverse compression a) and associated damage scenario b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
We could have thought, upon first glance, that without the presence of a positive principal stress the fracture would come as a result of shearing. If that had been the case, we then would have observed a crack at 45° (the direction of maximum shear stress is at 45° from the compression direction).
Mohr–Coulomb emitted the hypothesis that this was indeed a shear fracture, only impeded by friction due to the negative normal stress; in other words, the more negative the normal stress, the more the material can endure shearing before breaking.
Figure 4.11. Shear fracture without a) and with b) compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
This crack will then cause a shear fracture of the fiber/matrix interface or the matrix. This eventually leads to a final break of the sample by shearing.
4.1.5. In-plane shear
During an in-plane shear test of a UD, we observe the appearance of cracks at 45° (the direction of maximum principal stress is at 45° of the shear direction) (Figure 4.12(b)).
These cracks will then develop and coalesce and then create a fracture facies composed of cusps which are typical of shear fracture (Figures 4.13 and 4.14).
Figure 4.12. In-plane shear loading a) and appearance of shear cracks along 45°-direction b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
Figure 4.13. In-plane fracture: creation of cusps. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
This type of fracture, like transverse tensile fracture, is highly critical for a UD but must obviously be avoided at the design stage of the structure. In practice, fibers at ±45° should be used to withstand these types of stress. In fact, it’s to avoid these types of fractures that there is at least 10% of fiber at ±45° even in the absence of shear stress. In other words, if this type of fracture occurs in a laminate it means that it was badly designed. We should always aim for the fibers to withstand the main loads and they will be the ones to govern the final fracture.
Figure 4.14. Shear fracture: creation of cusps in a carbon/epoxy UD [ROG 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
In practice, the loading of a UD composite is complicated and reveals a number of stress states; its fracture is therefore a combination of these different basic fracture modes.
4.2. Fracture of a laminate
A laminate being an assembly of UD plies, its fracture mechanisms will, for each ply, regroup the elementary fracture mechanisms previously mentioned. However, we will also see the appearance of a potential splitting of the interface between layers, called delamination.
Figure 4.15. Different fracture modes of composites [EVE 99]
Another mode of fracture of the UD ply that has not been previously mentioned can also appear: out-of-plane fracture. For a laminate, especially a thick one, out-of-plane stress, in particular that resulting from out-of-plane transverse shear τtz, can become very intense and cause the fracture of plies of the laminate. Furthermore, we note that there is a high interaction between out-of-plane matrix cracking and delamination: when a matrix crack reaches an interface, it initiates delamination.
Figure 4.16. Matrix cracking in transverse tension a) and shearing b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
The characteristics of out-of-plane shearing are more difficult to obtain and we generally use three point bending tests, even if the results should be taken with a grain of salt.
Figure 4.17. Characterization test of composite under out-of-plane shearing. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
EXAMPLE (Fracture of a quasi-isotropic laminate).– If we perform a tensile test of a quasi-isotropic laminate [0,45,90,–45]S (see Chapter 8), the first plies to break are along 90°-direction due to transverse cracking (Figure 4.18). This fracture is obviously not critical as most of the load is withstood by the plies along 0 °-direction. At the same time, a few isolated fibers at 0° will break, mainly the ones that are badly oriented and/or more brittle than the average. Secondly, the plies at ±45° will break from transverse cracking and in-plane shearing. Once again, this fracture is not critical. At the same time, isolated fibers will continue to fracture. Finally, the plies at 0° will break, leading to the ultimate fracture.
Figure 4.18. Damage scenario of a quasi-isotropic laminate
EXAMPLE (Fracture of a laminate [45,–45]S).– If we perform a tensile test of a laminate [45,–45]S (see Chapter 8), we first observe the matrix cracking of ±45° plies, primarily due to in-plane shear stress τlt, followed by delamination between layers that leads to ultimate fracture.
